A simple and general methodology to calibrate seismic instruments for debris flow quantification: application to Cotopaxi and Tungurahua volcanoes (Ecuador)

Debris flows are hazardous phenomena occurring at volcanoes, and monitoring them has proved as challenging as imperative in several cases. The use of seismic instruments to measure and study the physical properties of debris flows has witnessed significant progress in the last years, with the use of improved sensors, innovative methodologies and high-resolution analysis. However, the application of such studies to the practical task of providing early warnings remains limited by the significant amount of infrastructural and technological resources commonly required for their deployment. In Ecuador, debris flows at volcanoes are detected by means of seismic instruments which are usually part of broader monitoring networks, thus requiring calibration to provide quantitative information about the flows and feed early-warning systems. In the present work, a theoretical approach based on the Buckingham Π-theorem is used to determine an expression that linearly correlates the seismic signal produced by a transiting debris flow with its discharge rate, for instruments installed in different substrata and at variable distances from the drainage. The expression is experimentally tested with Acoustic Flow Monitors and Broad-band seismometers installed in the vicinity of drainages at Tungurahua and Cotopaxi volcanoes, where actual debris flows occurred in relation to eruptive activity. The experiments consist in comparing the measured peak amplitude values of the seismic signal envelopes with the estimated peak discharge rates of several events. The results confirm the validity of the theoretical expression with linear correlations observed between the seismic amplitudes and the discharge rates, thus defining calibration expressions that can be generally applied to varied environments and instruments. The seismic instruments calibrated through this methodology can provide instantaneous and reliable predictions of debris flow discharge rates within less than an order of magnitude and only requiring limited data processing and storage. Such level of prediction could help to improve early warning systems based on seismic instruments installed in locations where more developed instrumental arrays are unavailable or unpractical.